diketahui fungsi f(x)=5-sin(2x+phi/4) cos (2x+phi/4). nilai minimum f(x)

Hai P, jawaban yang benar adalah 5. Konsep: Misalkan diketahui f(x) = k - sin a cos a maka f(x) = k - 1/2 sin 2a f'(x) = - cos 2a cos x = cos α 1) x = α + k . 2π 2) x = -α + k . 2π Diketahui f(x) = 5 - sin(2x + π/4) cos (2x + π/4) sehingga f'(x) = - cos (2x + π/4) diperoleh - cos (2x + π/4) = 0 cos (2x + π/4) = 0 cos (2x + π/4) = cos π/2 1) 2x + π/4 = π/2 + k . 2π 2x = π/2 - π/4 + k . 2π 2x = π/4 + k . 2π x = π/8 + k . π k = 0 maka x = π/8 2) 2x + π/4 = - π/2 + k . 2π 2x = - π/2 - π/4 + k . 2π 2x = -3π/4 + k . 2π x = -3π/4 + k . π k = 0 maka x = -3π/4 Oleh karena itu f(π/8) = 5 - sin(2(π/8) + π/4) cos (2(π/8) + π/4) f(π/8) = 5 - sin(π/4 + π/4) cos (π/4 + π/4) f(π/8) = 5 - sin(π/2) cos (π/2) f(π/8) = 5 - (1)(0) f(π/8) = 5 dan f( -3π/4) = 5 - sin(2( -3π/4) + π/4) cos (2( -3π/4) + π/4) f( -3π/4) = 5 - sin(-3π/2 + π/4) cos (-3π/2 + π/4) f( -3π/4) = 5 - sin(-5π/4) cos (-5π/4) f( -3π/4) = 5 - (1/2 √2)(- 1/2 √2) f( -3π/4) = 5 - (- 1/2) f( -3π/4) = 5½ Dengan demikian, nilai minimum f(x) adalah 5. Semoga membantu ya :)